A day after Aaron Hill had a home run washed out when the game at Citi Field was postponed because of rain, he cracked a key hit that counted. His second-inning double set up run-scoring singles by Prado and Cody Ross that put Arizona ahead to stay.
David Wright homered, doubled and singled for the Mets.
Collmenter (3-2) won his third decision in a row over a span of six starts. The righty with the unusual, straight over-the-top delivery allowed two runs in six innings before the Arizona bullpen held on.
Addison Reed pitched a perfect ninth for his 13th save in 15 chances. The Diamondbacks improved to 11-9 since a discouraging 8-22 start.
Zack Wheeler (1-5) is now winless in seven starts. His lone victory came in mid-April when he won at Phoenix in Collmenter's first start of the year.
Wheeler's control troubles have hurt him this year. A leadoff walk in the second led to Arizona scoring twice, and Wheeler later hit two batters.
Hill doubled off the left-center wall in the second, near the spot where he cleared the fence Friday night for a two-run homer. The stats from that game were wiped away when it was stopped in the fourth inning because of heavy showers, forcing a doubleheader Sunday.
Prado's RBI single in the third came after a throwing error by shortstop Wilmer Flores and made it 3-0 as a light rain fell on and off.
Curtis Granderson hit an RBI double in the Mets third after singles by Murphy and Wright.
Wright connected in the fifth for his third home run of the season.
NOTES: Arizona RHP Bronson Arroyo (4-3, 4.45) will start Game 1 Sunday against RHP Rafael Montero (0-2, 6.97). The Diamondbacks will promote RHP Zeke Spruill from Triple-A to make his season debut in the majors in the second game vs. RHP Daisuke Matsuzaka (1-0, 2.14). Matsuzaka hasn't started this year. ... Righty reliever Vic Black will join the Mets as the 26th man for the doubleheader. He throws hard, but can be wild. ... Mets LF Chris Young rammed into the wall padding while catching Hill's drive in the fifth. ... Mets RHP Bartolo Colon turned 41, a day after pitching four innings in the rainout. He's giving up home runs at much higher rate than usual, and manager Terry Collins said pitch location is the problem. ... Opponents are hitting .355 (21 for 59) against Wheeler with runners in scoring position. ... Collmenter struck out Lucas Duda with the bases loaded to end the first. The Mets are hitting just .143 (6 for 42) with the bases loaded this season.